SIR J. COCKLE ON MATHEMATICAL HISTORY. 13 



it necessary to consider whether pressure does or does not 

 tend to produce motion. Lagrange (Mec. An. i. 19) 

 thinks that the principle of the composition of forces, in 

 being separated from that of the composition of motions, 

 loses its principal advantages ; and he, just before saying 

 this, throws out a doubt as to whether a principle used by 

 Daniel Bernoulli in his demonstration was altogether inde- 

 pendent of the conception of motion. The whole subject 

 of composition is discussed by De Morgan in his paper " On 

 the General Principles of which the Composition or Ag- 

 gregation of Forces is a consequence " (Camb. Trans, 

 vol. X. part ii. 1859). 



8. Lagrange (Mec. An. i. p. 14, No. 11) observes that, 

 although the principles of the lever and of composition 

 lead always to the same results, it is remarkable that the 

 simplest case for the one becomes the most complicated for 

 the other. He adds [ib. No. 12) that we can establish an 

 immediate connexion between these two principles by a 

 theorem of Varignon. Newton's view is noticed by La- 

 grange {ib. No. 10). 



9. Thomson and Tait have a special object (Treatise, 

 vol. i. Preface, p. v, p. 141. par. (f), p. 341- § ASZ), 

 in reference to which Newton's proof may be the more 

 appropriate or elegant. I here use the word " elegant " in 

 the sense in which Austin, in his ' Lectures on Jurisprudence' 

 (vol. ii. p. 365), says it is used by the Roman lawyers. 

 But there is much that is interesting in the other investi- 

 gations on the subject. 



10. Lagrange [ib. p. 29) uses the word "moment" in 

 the sense which Galileo {ib. p. 20) gave to it, viz. the pro- 

 duct of the force into its virtual velocity, noticing, however, 

 another {ib. p. 7) meaning, viz. the product of the force 

 into the arm of the lever by which it acts. 



11. Whewell (Hist. Ind. Sci. i. p. 93), speaking of a 



